Can a Tensorflow variable be trained using the Tensorflow keras functional API?

I am wondering if Keras model compile/training with the functional API train variables defined by tf.get_variable? Can Keras training also incorporate Tensorflow operations?

BackGround

It looks like since Tensorflow is the backend, there are ways to mix Keras/Tensorflow variables. This blog post shows how Keras variables are trained using a Tensorflow graph/session https://blog.keras.io/keras-as-a-simplified-interface-to-tensorflow-tutorial.html

from keras.layers import Dropout
from keras import backend as K

img = tf.placeholder(tf.float32, shape=(None, 784))
labels = tf.placeholder(tf.float32, shape=(None, 10))

x = Dense(128, activation='relu')(img)
x = Dropout(0.5)(x)
x = Dense(128, activation='relu')(x)
x = Dropout(0.5)(x)
preds = Dense(10, activation='softmax')(x)

loss = tf.reduce_mean(categorical_crossentropy(labels, preds))

train_step = tf.train.GradientDescentOptimizer(0.5).minimize(loss)
with sess.as_default():
    for i in range(100):
        batch = mnist_data.train.next_batch(50)
        train_step.run(feed_dict={img: batch[0],
                                  labels: batch[1],
                                  K.learning_phase(): 1})

acc_value = accuracy(labels, preds)
with sess.as_default():
    print acc_value.eval(feed_dict={img: mnist_data.test.images,
                                    labels: mnist_data.test.labels,
                                    K.learning_phase(): 0})

And also here it shows that Tensorflow variables can be used as input to a Keras model

How to set the input of a Keras layer of a functional model, with a Tensorflow tensor?

tf_embedding_input = ...    # pre-processing output tensor

# Keras model
model = Sequential()
model.add(Input(tensor=tf_embedding_input)) 
model.add(Embedding(max_features, 128, input_length=maxlen))

So I am wondering if Keras can train Tensorflow variables.

Example

I would like to train the embedding and softmax variables in the Tensorflow architecture below

  embeddings = tf.get_variable( 'embeddings', 
    initializer= tf.random_uniform([vocabulary_size, embedding_size], -1.0, 1.0))

  softmax_weights = tf.get_variable( 'softmax_weights',
    initializer= tf.truncated_normal([vocabulary_size, embedding_size],
                         stddev=1.0 / math.sqrt(embedding_size)))

  softmax_biases = tf.get_variable('softmax_biases', 
    initializer= tf.zeros([vocabulary_size]),  trainable=False )

  embed = tf.nn.embedding_lookup(embeddings, train_dataset) #train data set is

  embed_reshaped = tf.reshape( embed, [batch_size*num_inputs, embedding_size] )

  segments= np.arange(batch_size).repeat(num_inputs)

  averaged_embeds = tf.segment_mean(embed_reshaped, segments, name=None)

  loss = tf.reduce_mean(
    tf.nn.sampled_softmax_loss(weights=softmax_weights, biases=softmax_biases, inputs=averaged_embeds,
                               labels=train_labels, num_sampled=num_sampled, num_classes=vocabulary_size))

Since Tensorflow Keras uses a Tensorflow backend, I'm guessing it's somehow possible to use and train Tensorflow variables and use Tensorflow operations in training.

Why do I want to do this?

Google's TPUs require that your architecture be implemented via the Estimator API or Keras API. So there is probably interest in converting a regular Tensorflow Graph/Session to use the Keras API with as few alterations to their code as possible.

Knowing how to incorporate Tensorflow operations and train Tensorflow variables using the Keras model compile/train would greatly help with this.

from Can a Tensorflow variable be trained using the Tensorflow keras functional API?